Mathematical Foundations of Artificial Intelligence Fairness in Algorithmic Credit Scoring for Nigerian Financial Inclusion

The rapid deployment of algorithmic credit scoring systems by Nigerian fintech companies and digital lenders to extend financial services to the unbanked population raises fundamental questions about mathematical fairness: whether automated lending decisions systematically disadvantage applicants from particular ethnic groups, geographic regions, or gender categories in ways that perpetuate exclusion rather than expand access. This dissertation develops mathematical foundations for AI fairness in the specific context of algorithmic credit scoring for financial inclusion in Nigeria, making original theoretical contributions to both the abstract theory of algorithmic fairness and its application to the Nigerian credit market. The first contribution establishes a novel impossibility theorem extending the Chouldechova-Kleinberg result to the multi-group, multi-threshold fairness framework characteristic of Nigerian credit market segmentation, proving that simultaneous satisfaction of calibration, equalised odds, and predictive parity across six defined demographic groups is mathematically impossible under conditions satisfied by observed credit score distributions. The second contribution develops a constrained empirical risk minimisation framework that navigates this impossibility by solving a Pareto-optimal fairness-accuracy trade-off problem, with a theoretically characterised efficient frontier. The framework is applied to proprietary credit application and repayment data from three Nigerian digital lenders covering 180,000 loan records from 2021 to 2023. Results demonstrate that applying the optimal fairness-constrained model increases credit approval rates for applicants from the North West and North East zones by 14 and 19 percent respectively relative to the unconstrained model, with accuracy loss of only 2.3 percent. Keywords: algorithmic fairness, credit scoring, financial inclusion, impossibility theorem, Nigeria.